Generalized ray method for three-dimensional propagation in a penetrable wedge

Abstract

A generalized ray solution is presented for the three-dimensional (3-D) acoustic field produced by a transient point source in a rigid-bottom, fast-speed fluid-bottom, and fast-speed elastic-bottom wedge modeling a continental shelf environment. The effect of diffraction (scattering) at the wedge apex is ignored in the solution, but nevertheless the solution is exact and complete for the image component of the field, expressed by a sum of partial waves including a pulse emitted from the source plus a finite number of pulses reflected off the wedge boundaries. Time records of the acoustic pressure illustrating 3-D acoustical propagation effects are evaluated at five receivers located at equal radial range in the horizontal from the source, but different orientation to the source, measured by the azimuthal angle assuming values: 0^{circ } (down-slope), 45^{circ } (obliquely down-slope), 90^{circ } (cross-slope), 135^{circ } (obliquely up-slope), and 180^{circ } (up-slope). The arrival times of the spherical and head waves propagating along various paths are evaluated at each receiver for each bottom. It was found that the time interval between the first arrival and the ultimate arrival diminished, and the pulses became more peaked, as the azimuthal angle of the receiver increased. For the rigid-bottom wedge, we have found that all backscattered pulses are significant at the up-slope receiver. For the fluid-bottom wedge, we have found that: at each receiver, the source-pulse is preceded by the ground wave which is much weaker than the water wave; and, at the up-slope receiver, the backscattered pulses are insignificant. For the elastic-bottom wedge, we have found that: at each receiver, the ground-wave-response begins earlier than that in the fluid-bottom wedge, and thus the record separates out into distinct ground-wave and water-wave phases; and, at the up-slope receiver, the backscattered pulses are significant.